# Figure 8.20, page 444.
# Floor planning example.

from cvxopt import solvers, matrix, spmatrix, mul, div
try: import pylab
except ImportError: pylab_installed = False
else: pylab_installed = True

def floorplan(Amin):

    #     minimize    W+H
    #     subject to  Amin1 / h1 <= w1 
    #                 Amin2 / h2 <= w2 
    #                 Amin3 / h3 <= w3 
    #                 Amin4 / h4 <= w4 
    #                 Amin5 / h5 <= w5 
    #                 x1 >= 0
    #                 x2 >= 0
    #                 x4 >= 0
    #                 x1 + w1 + rho <= x3  
    #                 x2 + w2 + rho <= x3 
    #                 x3 + w3 + rho <= x5  
    #                 x4 + w4 + rho <= x5
    #                 x5 + w5 <= W
    #                 y2 >= 0  
    #                 y3 >= 0  
    #                 y5 >= 0 
    #                 y2 + h2 + rho <= y1 
    #                 y1 + h1 + rho <= y4 
    #                 y3 + h3 + rho <= y4
    #                 y4 + h4 <= H  
    #                 y5 + h5 <= H
    #                 h1/gamma <= w1 <= gamma*h1
    #                 h2/gamma <= w2 <= gamma*h2
    #                 h3/gamma <= w3 <= gamma*h3
    #                 h4/gamma <= w4 <= gamma*h4
    #                 h5/gamma <= w5 <= gamma*h5
    #
    # 22 Variables W, H, x (5), y (5), w (5), h (5).
    #
    # W, H:  scalars; bounding box width and height
    # x, y:  5-vectors; coordinates of bottom left corners of blocks
    # w, h:  5-vectors; widths and heigths of the 5 blocks

    rho, gamma = 1.0, 5.0   # min spacing, min aspect ratio

    # The objective is to minimize W + H.  There are five nonlinear 
    # constraints 
    #
    #     -w1 + Amin1 / h1 <= 0 
    #     -w2 + Amin2 / h2 <= 0 
    #     -w3 + Amin3 / h3 <= 0 
    #     -w4 + Amin4 / h4 <= 0 
    #     -w5 + Amin5 / h5 <= 0.

    c = matrix(2*[1.0] + 20*[0.0])

    def F(x=None, z=None):
        if x is None:  
            return 5, matrix(17*[0.0] + 5*[1.0])
        if min(x[17:]) <= 0.0:  
            return None 
        f = -x[12:17] + div(Amin, x[17:]) 
        Df = matrix(0.0, (5,22))
        Df[:,12:17] = spmatrix(-1.0, range(5), range(5))
        Df[:,17:] = spmatrix(-div(Amin, x[17:]**2), range(5), range(5))
        if z is None: 
            return f, Df
        H = spmatrix( 2.0* mul(z, div(Amin, x[17::]**3)), range(17,22), 
            range(17,22) )
        return f, Df, H

    # linear inequalities
    G = matrix(0.0, (26,22)) 
    h = matrix(0.0, (26,1))

    # -x1 <= 0
    G[0,2] = -1.0   

    # -x2 <= 0
    G[1,3] = -1.0   

    # -x4 <= 0
    G[2,5] = -1.0   

    # x1 - x3 + w1 <= -rho 
    G[3, [2, 4, 12]], h[3] = [1.0, -1.0, 1.0], -rho

    # x2 - x3 + w2 <= -rho 
    G[4, [3, 4, 13]], h[4] = [1.0, -1.0, 1.0], -rho
 
    # x3 - x5 + w3 <= -rho 
    G[5, [4, 6, 14]], h[5] = [1.0, -1.0, 1.0], -rho 

    # x4 - x5 + w4 <= -rho 
    G[6, [5, 6, 15]], h[6] = [1.0, -1.0, 1.0], -rho 

    # -W + x5 + w5 <= 0
    G[7, [0, 6, 16]] = -1.0, 1.0, 1.0

    # -y2 <= 0  
    G[8,8] = -1.0

    # -y3 <= 0  
    G[9,9] = -1.0

    # -y5 <= 0 
    G[10,11] = -1.0

    # -y1 + y2 + h2 <= -rho 
    G[11, [7, 8, 18]], h[11] = [-1.0, 1.0, 1.0], -rho 

    # y1 - y4 + h1 <= -rho 
    G[12, [7, 10, 17]], h[12] = [1.0, -1.0, 1.0], -rho 

    # y3 - y4 + h3 <= -rho 
    G[13, [9, 10, 19]], h[13] = [1.0, -1.0, 1.0], -rho 

    # -H + y4 + h4 <= 0  
    G[14, [1, 10, 20]] = -1.0, 1.0, 1.0

    # -H + y5 + h5 <= 0
    G[15, [1, 11, 21]] = -1.0, 1.0, 1.0

    # -w1 + h1/gamma <= 0 
    G[16, [12, 17]] = -1.0, 1.0/gamma

    # w1 - gamma * h1 <= 0
    G[17, [12, 17]] = 1.0, -gamma

    # -w2 + h2/gamma <= 0 
    G[18, [13, 18]] = -1.0, 1.0/gamma 

    # w2 - gamma * h2 <= 0
    G[19, [13, 18]] = 1.0, -gamma

    # -w3 + h3/gamma <= 0  
    G[20, [14, 19]] = -1.0, 1.0/gamma

    # w3 - gamma * h3 <= 0
    G[21, [14, 19]] = 1.0, -gamma

    # -w4  + h4/gamma <= 0 
    G[22, [15, 20]] = -1.0, 1.0/gamma

    # w4 - gamma * h4 <= 0
    G[23, [15, 20]] = 1.0, -gamma

    # -w5 + h5/gamma <= 0 
    G[24, [16, 21]] = -1.0, 1.0/gamma

    # w5 - gamma * h5 <= 0.0
    G[25, [16, 21]] = 1.0, -gamma

    # solve and return W, H, x, y, w, h 
    sol = solvers.cpl(c, F, G, h)
    return  sol['x'][0], sol['x'][1], sol['x'][2:7], sol['x'][7:12], \
        sol['x'][12:17], sol['x'][17:] 

#solvers.options['show_progress'] = False

if pylab_installed: pylab.figure(facecolor='w')

Amin = matrix([100., 100., 100., 100., 100.])
W, H, x, y, w, h =  floorplan(Amin)
if pylab_installed:
    if pylab_installed: pylab.subplot(221)
    for k in range(5):
        pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]], 
                   [y[k], y[k]+h[k], y[k]+h[k], y[k]], 
                   facecolor = '#D0D0D0', ec='k')
        pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
    pylab.axis([-1.0, 26, -1.0, 26])
    pylab.xticks([])
    pylab.yticks([])

Amin = matrix([20., 50., 80., 150., 200.])
W, H, x, y, w, h =  floorplan(Amin)
if pylab_installed:
    pylab.subplot(222)
    for k in range(5):
        pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]], 
                   [y[k], y[k]+h[k], y[k]+h[k], y[k]], 
                   facecolor = '#D0D0D0', ec = 'k')
        pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
    pylab.axis([-1.0, 26, -1.0, 26])
    pylab.xticks([])
    pylab.yticks([])

Amin = matrix([180., 80., 80., 80., 80.])
W, H, x, y, w, h =  floorplan(Amin)
if pylab_installed:
    pylab.subplot(223)
    for k in range(5):
        pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]], 
                   [y[k], y[k]+h[k], y[k]+h[k], y[k]], 
                   facecolor = '#D0D0D0', ec = 'k')
        pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
    pylab.axis([-1.0, 26, -1.0, 26])
    pylab.xticks([])
    pylab.yticks([])
    
Amin = matrix([20., 150., 20., 200., 110.])
W, H, x, y, w, h =  floorplan(Amin)
if pylab_installed:
    pylab.subplot(224)
    for k in range(5):
        pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]], 
                   [y[k], y[k]+h[k], y[k]+h[k], y[k]], 
                   facecolor = '#D0D0D0', ec = 'k')
        pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
    pylab.axis([-1.0, 26, -1.0, 26])
    pylab.xticks([])
    pylab.yticks([])

    pylab.show()
